3. What is your greatest weakness?

[...] Don’t lie, but instead prepare to answer with a “weakness” that’s actually a strength. Say, “I am a perfectionist who is always striving for excellence, even when it means I push myself too hard on a project.” Or “I’m driven to make my team the best, most successful sales team. This means the people working for me need to have aspirational goals as well.”

These behaviors are ones that will be perceived as strengths, assuming they are what’s needed in the role you will be playing.

If I can't be completely honest with an employer because they're going to always assume I'm presenting myself in my best light (and therefore if I'm honest with them about a weakness, the reality must be even worse), do I really want to work for them??

...other than for reasons of economic coercion, of course, which is what this is ultimately all about: the employer wants to know how hard you're going to try to compromise your principles on their behalf, because that's a signal of future obedience.

They want to know that you'll grind yourself down to the metal pretending you don't have any real flaws -- that you'll side with the strong over the weak rather than reveal your own weaknesses, and thus help them preserve their power.